If A non-singular matrix such that `(A-2l)(A-4l)=0` then A=`8A^(-1)=` . .

Options

A. I
B. 0
C. 3I
D. 6I

Answer

D

Explanation

We have `absAne0`
`rArrA^(-1)` is exists
Since,(A-2I)(A-4I)=0
`rArrA^(2)-A(4I)-2I(A)+8IdotI=0`
`rArrA^(2)-4AI-2AI+8I=0`
`rArrA^(2)-6AI+8I=0`
`rArrA^(2)-6A+8I=0`
On pre multiply both sides by `A^(-1)`, we get
`A^(-1)A^(2)-6A^(-1)A+8A^(-1)I=0`
`rArrIA-6I+8A^(-1)`=0
`rArrA-6I+8A^(-1)=0`
`rArrA+8A^(-1)=6I`